1.For RL series circuit R = 4 and L = 0.5 H. The source voltage V = 12 Vdc is ap

1.For RL series circuit R = 4 and L = 0.5 H. The source voltage V = 12 Vdc is applied. Find the current i(t) using the Laplace transform. Assume all initialconditions are zeros.a) First write the voltage equation in terms of a differential equation. b) Second apply the Laplace transform on the equation. For example if you take the Laplace transform on V = 12 V then the Laplace transform of 12 = 12/sthe Laplace transform of i(t) =I(s) etc. c) Rearrange the transformed equation for the current I(s). d) Take the inverse Laplace transform of I(s) to find the current i(t). e) The answer should be i(t) = 3(1-e^(-8t)). f) From the answer (e) what is the transient and the final (stable or steady-state) value? Describe i(t) from (e) more specifically. g) What is the time constant of the circuit? Calculate it.